Question

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Answer 1

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Answer:

  D.  2%  

Step-by-step explanation:

The growth rate can be found by looking at the growth factor of the exponential function.

  f(x) = (initial value) × (growth factor)^x

The growth rate is related by ...

  growth factor = growth rate + 1

This means the growth rate of f(x) is 1.04 -1 = 0.04 = 4%.

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We can write the function g(x) describing the table as ...

  g(x) = (value at x=x1) × ((value at x=x2)/(value at x=x1))^((x-x1)/(x2-x1))

So, this could be ...

  g(x) = 31.21 × (32.47/31.21)^((x-2)/2) = a·b^x

     where b = (32.47/31.21)^(1/2) ≈ 1.02 . . . . growth factor

This means the growth rate for g(x) is 1.02 -1 = 0.02 = 2%.

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Then the difference between the growth rates of the two functions is ...

  4% - 2% = 2% . . . . . matches choice D